PHYSICAL REVIEW APPLIED 10, 024001 (2018) Self-Injection Locking of a Spin Torque Nano-Oscillator to Magnetic Field Feedback Hanuman Singh, 1 A. Bose, 1 S. Bhuktare, 1 A. Fukushima, 2 K. Yakushiji, 2 S. Yuasa, 2 H. Kubota, 2 and Ashwin A. Tulapurkar 1, ∗ 1 Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India 2 National Institute of Advanced Industrial Science and Technology (AIST), Spintronics Research Center, Ibaraki 305-8568, Japan (Received 4 February 2018; revised manuscript received 5 March 2018; published 1 August 2018) We demonstrate the self-synchronization of a spin torque nano-oscillator (STNO) using magnetic field feedback. The rf output of the STNO is connected to a waveguide which rests on top of the magnetic tunnel junction (MTJ). The resulting rf current flowing through the waveguide creates a magnetic field on the free layer of the MTJ, which acts as the feedback. We observe a large improvement in the qual- ity factor as the feedback strength is increased. Our results indicate a transition to an oscillatory state dominated by feedback at higher feedback strength. We also explore the effect of feedback phase on mag- netization oscillation by inserting an adjustable delay in the feedback path. The experimental results are qualitatively supported by macromagnetic simulation. Our results open an alternative avenue to control the magnetization dynamics of a nanomagnet. DOI: 10.1103/PhysRevApplied.10.024001 I. INTRODUCTION The spin-transfer-torque (STT) effect [1,2] can be used to manipulate the magnetization direction of a nanomag- net. Nanoscale oscillators based on the STT effect [spin torque nano-oscillators (STNO)] [3–9] have been exten- sively studied due to the application possibilities as well as the novel physics involved. STT oscillators can be classified into two types depending on how the spin cur- rent is produced: (i) based on magnetic tunnel junctions (MTJs) (or spin valves), where spin current is produced by charge current passing through the fixed layer and (ii) spin- Hall-effect-based oscillators [10–14], where spin current is produced by the spin Hall effect in a heavy metal. Recently, spintronic feedback nano-oscillators (SFNO) based on the magnetic field feedback effect [15,16] have been demon- strated. These types of oscillators do not need STT, but are based on the tunneling magnetoresistance (TMR) effect. Small output power and large line width are major chal- lenges for STNO devices. The line width of STNO output can be reduced if we can control the phase of the oscil- lation. It is well known that the phase of an oscillator can be stabilized by locking it to an external oscillating force [17–28], which is called as injection locking. If the oscillator output itself plays the role of external force, the effect is called self-injection locking. This idea has been explored theoretically [29] and also shown experimentally * ashwin@ee.iitb.ac.in [30] in the case of a vortex-based oscillator by feeding the output rf current back into the STNO, which results in a spin-current feedback. Here we demonstrate a dif- ferent mechanism for feedback. We use the rf output of the STNO to generate magnetic field, which provides the delayed feedback. To demonstrate the self-injection lock- ing of the STNO, we fabricate a waveguide on top of a MTJ. A bias dc current is passed through the MTJ to induce the STT oscillations. The rf output voltage of the MTJ is connected to the waveguide through an amplifier, which results in passage of rf current through the waveguide. The rf magnetic field created by the current in the waveguide provides the feedback for self-injection locking. In Ref. [16], we used the magnetic field feedback to generate rf oscillations without any help from spin-transfer torque, whereas in this work we use magnetic field feedback to control the phase of a spin-torque oscillator. Our method of feedback has the advantage that we can control the feed- back strength by changing the gain of the amplifier. This allows us to study the oscillator power and quality factor as a function of the feedback strength, which was not pos- sible in the previous experiments. The experimental results with higher gain show that the feedback no longer merely controls the phase of oscillation, but changes the shape of power spectral density considerably. II. EXPERIMENTAL METHOD The MTJ stack is fabricated on a thermally grown SiO 2 (500 nm) with the following structure: bottom contact 2331-7019/18/10(2)/024001(6) 024001-1 © 2018 American Physical Society